Geometrical relations between space time block code designs and complexity reduction

TL;DR

This paper explores the geometric relationships between coherent and non-coherent space-time block codes, providing bounds and design criteria that simplify code development and enhance performance understanding.

Contribution

It introduces a geometric framework linking coherent and non-coherent codes, offering a performance bound and a decomposition approach for code design.

Findings

Derived a lower bound on non-coherent code performance in coherent channels.

Proposed a code design decomposition into two simpler sub-tasks.

Established a geometric criterion for high-performance space-time codes.

Abstract

In this work, the geometric relation between space time block code design for the coherent channel and its non-coherent counterpart is exploited to get an analogue of the information theoretic inequality $I(X;S)\le I((X,H);S)$ in terms of diversity. It provides a lower bound on the performance of non-coherent codes when used in coherent scenarios. This leads in turn to a code design decomposition result splitting coherent code design into two complexity reduced sub tasks. Moreover a geometrical criterion for high performance space time code design is derived.